<PAGE>   1

                                                                 EXHIBIT 10.6.3

                         SECOND AMENDMENT TO AGREEMENT

         THIS SECOND AMENDMENT TO AGREEMENT, made as of the 17th day of
January, 1995, by and between Dillon Companies, Inc. ("Shareholder") and E-Z
Serve Convenience Stores, Inc. ("E-Z").

                             W I T N E S S E T H :

         WHEREAS, Dillon and E-Z are parties to an Agreement dated as of
December 2, 1994, as amended by Amendment to Agreement dated as of December 28,
1994, pursuant to which E-Z is to acquire the common stock of Time Saver
Stores, Inc., on the terms and conditions set forth in the Agreement; and

         WHEREAS, the parties desire to modify and amend the Agreement as set
forth below;

         NOW, THEREFORE, in consideration of the mutual agreements contained
herein, the parties agree as follows:

1.       Capitalized terms used herein shall have the meanings ascribed to them
         in the Agreement.

2.       E-Z has conducted a lien and judgment search on Time Saver and Delight
         which has disclosed the liens and judgments attached hereto as
         Schedule 1 (the "Judgments").  Shareholder believes that all of the
         Judgments have been satisfied.  Shareholder shall use its best efforts
         to deliver to E-Z, on or before the date of delivery of the Closing
         Financial Statements, documentation evidencing the
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         satisfaction of the Judgments and the release of record of judgment
         liens associated therewith.  In the event that Shareholder is unable
         to furnish such documentation, it shall indemnify E-Z with respect to
         such Judgments as to which documentation is not furnished, to the same
         extent as set forth in Article 9 of the Agreement.

3.       Except as otherwise modified herein, the Agreement shall remain
         unchanged and in full force and effect.

         IN WITNESS WHEREOF, the parties hereto, intending to be legally bound,
have signed this Agreement as of the day and year first above written.

                                        DILLON COMPANIES, INC.

                                        By: /s/ FRANK J. REMAR 
Attest:                                    -------------------------------------
                                           Frank J. Remar
                                           Senior Vice President

 /s/ ROBERT L. MEYERS
--------------------------------
         Vice President



                                        E-Z SERVE CONVENIENCE STORES, INC.


                                        By: /s/ JOHN T. MILLER 
                                           -------------------------------------
                                           John T. Miller
                                           Senior Vice President
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E-Z SERVE CORPORATION joins in the execution hereof for the purposes of
consenting hereto and unconditionally guarantying the performance and
undertakings of E-Z under this Second Amendment to Agreement.

                                        E-Z SERVE CORPORATION


                                        By: /s/ JOHN T. MILLER 
                                           -------------------------------------
                                           John T. Miller
                                           Senior Vice President


STATE OF NEW YORK
                                        ) SS.
COUNTY OF NEW YORK

BE IT REMEMBERED, That on this 17th day of January, 1995, before me, a Notary
Public in and for said County and State, personally appeared Frank J. Remar,
and Robert L. Meyers, Senior Vice President and Vice President, respectively,
of DILLON COMPANIES, INC., the corporation, whose name is subscribed to and
which executed the foregoing instrument, and for themselves and as such
officers respectively, and for and on behalf of the corporation, acknowledged
the signing and execution of said instrument as their free and voluntary act
and deed as such officers respectively, and the free and voluntary act and deed
of said corporation, for the uses and purposes therein mentioned.

         IN TESTIMONY WHEREOF, I have hereunto subscribed my name and affixed
my official seal, on the day and year last aforesaid.

                                        /s/ BERNADETTE M. COLGAN               
                                        --------------------------------       
                                        Notary Public                          
My Commission Expires:                                                         
                                              BERNADETTE M. COLGAN             
                                        Notary Public, State of New York       
                                                 No. 03-5028006                
                                            Qualified in Bronx County          
                                        Commission Expires: May 23, 1996       
                                                                               
                                                                               
STATE OF NEW YORK
                                        ) SS.
COUNTY OF NEW YORK

         BE IT REMEMBERED, That on this 17th day of January, 1995, before me, a
Notary Public in and for said County and State, personally appeared John T.
Miller, Senior Vice President of E-Z Serve Convenience Stores, Inc., the
corporation, whose name is subscribed to and which executed the foregoing
instrument, and for themselves and as such officers respectively, and for and
on behalf of the corporation, acknowledged the signing and execution of said
instrument as their free and voluntary act and deed as such officers
respectively, and the free and voluntary act and deed of said corporation, for
the uses and purposes therein mentioned.
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         IN TESTIMONY WHEREOF, I have hereunto subscribed my name and affixed
my Notarial seal, on the day and year last aforesaid.



                                        /s/ BERNADETTE M. COLGAN               
                                        --------------------------------       
                                        Notary Public                          
My Commission Expires:                                                         
                                              BERNADETTE M. COLGAN             
                                        Notary Public, State of New York       
                                                 No. 03-5028006                
                                            Qualified in Bronx County          
                                        Commission Expires: May 23, 1996       
                                                                               
                                                                               
STATE OF NEW YORK
                         SS.
COUNTY OF NEW YORK

BE IT REMEMBERED, That on this 17th day of January, 1995, before me, a Notary
Public in and for said County and State, personally appeared John T.
Miller, Senior Vice President of E-Z Serve Corporation, the corporation, whose
name is subscribed to and which executed the foregoing instrument, and for
themselves and as such officers respectively, and for and on behalf of the
corporation, acknowledged the signing and execution of said instrument as their
free and voluntary act and deed as such officers respectively, and the free and
voluntary act and deed of said corporation, for the uses and purposes therein
mentioned.

         IN TESTIMONY WHEREOF, I have hereunto subscribed my name and affixed
my Notarial seal, on the day and year last aforesaid.


                                        /s/ BERNADETTE M. COLGAN               
                                        --------------------------------       
                                        Notary Public                          
My Commission Expires:                                                         
                                              BERNADETTE M. COLGAN             
                                        Notary Public, State of New York       
                                                 No. 03-5028006                
                                            Qualified in Bronx County          
                                        Commission Expires: May 23, 1996